1. Field of the Invention
The invention relates to a pre-modulation filter with an overall impulse response having the value k(t)=f(t).multidot.w(t), where f(t) represents the impulse response of the filter, and w(t) represents a window function determining a finite width of the overall impulse response.
2. Related Art
A pre-modulation filter of this structure, in which f(t) represents the untruncated impulse response g(t) of the pre-modulation filter, is known from the U.S. Pat. No. 4,229,821.
As described in the above Patent such a pre-modulation filter is used in combination with a modulator of a transmitter for transmitting an angle-modulated carrier signal of a substantially constant amplitude. Such a transmitter is generally intended to transmit binary data signals at a given symbol rate 1/T to a receiver through a transmission channel having a limited bandwidth.
In systems for transmission over radio links the modulation techniques should exhibit the most efficient use of the bandwidth of an available transmission channel. Even if a modulation technique resulting in an angle-modulated carrier signal of a continuous phase is used, the spectrum of this angle-modulated carrier signal will, nevertheless, generally be wider than that of the equivalent baseband signal. Limiting this spectrum by means of a channel filter is an unattractive solution for radio communication systems, since the practical implementation of such a channel filter having accurately prescribed amplitude and phase characteristics and usually a very small relative bandwidth in the radio frequency range, is extremely difficult and requires a high transmission power. In addition, numerous systems are of the multi-channel type, in which the carrier frequency to be transmitted is to be able to assume a relatively large number of different values. Therefore, the spectrum of the angle-modulated carrier signal in radio communication systems is generally restricted by means of pre-modulation techniques.
A further requirement on modulation techniques for radio communication systems is the fact that the corresponding detection techniques should result in an error chance as a function of the signal-to-noise ratio, which degrades as little as possible with respect to the error chance for optimum baseband transmission of the relevant data signals.
As further explained in the above Patent, such a pre-modulation filter can be considered to be a cascade arrangement of an encoding circuit and a low-pass filter. Such an encoding circuit has a partial response. Such a response can simply be described as a polynomial with the aid of the (algebraic) delay operator D for a delay over a symbol interval T, where D.sup.k represents a delay over k-symbol periods and I=D.sup.0 is an identity operator. For further details about such polynomials reference is made to an article by P. Kabal et al, entitled "Partial-Response Signalling", published in IEEE trans. Commun., Vol. COM-23, No. 9, pp. 921-924, September 1975.
As appears from the above U.S. Patent it holds for several of such polynomials that the phase .phi.(t) of the angle-modulated signal that develops at the output of a modulator which is combined with such a pre-modulation filter, exhibits a smooth and gradual variation as a function of time. This implies that the efficiency of the available frequency spectrum is improved because the power outside the frequency band of the spectral main lobe is decreased considerably. For all the cases considered in the above-mentioned U.S. Patent it was assumed that the low-pass filter fulfils the Nyquist criterion I or III, depending on whether the modulator for which this filter is intended is a phase modulator or a frequency modulator. The Patent also states that it is practically advantageous to realise a pre-modulation filter as a digital transversal filter. In this respect it is observed that despite the finite duration of the impulse response of a digital transversal filter, its transfer function is a good approximation of the transfer function that is desired. The effect of such a restriction of the duration of the impulse response on the power density spectrum of a modulator output signal is illustrated graphically. The variation in the provided graphs implies that a rectangular window function is utilized.
However, in the above-mentioned U.S. Patent, there is no further discussion of the attendant consequences of the use of truncation of the impulse response of such a filter with respect to the variation of the phase .phi.(t) of the angle-modulated signal that is generated at the output of the modulator. The effect of the power density spectrum is also compared exclusively on the basis of the width to which the impulse response is restricted.
In an article by F. de Jager et al., entitled "Tamed Frequency Modulation, A Novel Method to Achieve Spectrum Economy in Digital Transmission", published in IEEE Trans. Commun., Vol. COM-26, No. 5, pp. 534-542, May 1978, attention is paid to a modulation technique of the type commonly referred to as TFM. Such a modulation technique can be characterized by a specific partial-response polynomial F(D) having the value F(D)=(1+D).sup.2. This article describes the implementation of such an encoding technique in combination with different truncation lengths 3T, 5T and 7T as they are provided by a low-pass filter in which a transfer function of the type commonly referred to as Racos (raised cosine) is incorporated. In this article the effect of the different truncation lengths on the spectral power density is considered.
A generalization of the modulation techniques described in the above literature is presented in an article by D. Muilwijk, entitled "Correlative Phase Shift Keying-A Class of Constant Envelope Modulation Techniques", published in IEEE Trans. Commun., Vol. COM-29, No. 3, pp. 226-236, March 1981. In this article various modulation techniques of the type commonly referred to as CORPSK are described and analysed. However, there is no further discussion of the effect which truncation of the impulse response has on the angle-modulated signal with substantially constant amplitude developed at the output of an associated modulator.